Research interests include homotopy
theory and its relationships to the study of manifolds, in particular in knot theory,
configuration spaces, and
transformation groups.
I have had three graduate students complete PhDs,
namely Matt Miller who studied orbit configuration spaces of Lens spaces,
Chad Giusti
who worked out a piecewise-linear version of Vassiliev theory, and Kristy
Pelatt who studied the homology of knot spaces.
I currently have one student working towards her PhD, namely Safia Chettih.

My teaching interests and practices
include creating context
to facilitate abstract reasoning, "putting problems first" in teaching
proofs, and giving frequent small assignments to foster independence
in advanced courses. After using some of these techniques in courses
for pre-service teachers, I have been getting heavily involved in a
number of efforts in K-12 mathematics education, especially in support
of implementation of the Common Core.